Simplify the following expression: $x = \dfrac{q^2 + 15q + 50}{q + 5} $
Answer: First factor the polynomial in the numerator. $ q^2 + 15q + 50 = (q + 5)(q + 10) $ So we can rewrite the expression as: $x = \dfrac{(q + 5)(q + 10)}{q + 5} $ We can divide the numerator and denominator by $(q + 5)$ on condition that $q \neq -5$ Therefore $x = q + 10; q \neq -5$